Question

Jordan Air Inc. has average inventory of $1,000,000. Its estimated annual sales are 15 million and the firm estimates its receivables collection period to be twice as long as its inventory conversion period. The firm pays its trade credit on time; its terms are net 30. The firm wants to decrease its cash conversion cycle by 10 days. It believes that it can reduce its average inventory to $900,000. Assume a 360-day year and that sales will not change. Cost of goods sold equal 80 percent of sales. By how much must the firm also reduce its accounts receivable to meet its goal of a 10-day reduction?

Answer 1

1) Average Inventory equivalent Sales = Sales x 80% = Cost of Goods Sold. So Average inventory = $1000000/80% = $12,50,000

2) Inventory Conversion Period ICP = Average Inventory / Annual Sales x 360 days = $12,50,000/$15,00,0000 x 360 = 30 days

3) Average Collection period ACP = 2 x 30 = 60 days

4) Average Receivables = Sales / (360 / ACP) = 15000000 / (360 / 60) = $25,00,000

5) Operating cycle = Inventory Conversion Period + Average Collection period OC = 30 + 60 = 90 days

6) Cash conversion cycle = Operating cycle – Average Payment Period CCC = OC – APP = 90 days – 30 days = 60 days

Here, The firm wants to decrease its cash conversion cycle by 10 days. ie the new CCC would be = 60 -10 = 50 days

Therefore, new

1) CCC = OC - APP or OC = CCC + APP = 50 + 30 = 80 days

2) ICP = ($900000 x 0.8) / $1500000 x 360 days = 27 days

3) OC = ICP + ACP ie. 80 = 27 + ACP ie. ACP = 80 - 27 = 53 days

4) Average Receivables = Sales / (360 / ACP) = $15000000 / (360/53) = $22,08,333

So, Reduction in Receivables = $25,00,000 - $22,08,333 = $291667 ie $291667 / $ 2500000 = 11.67%